I'm not blind/VI either but I've played D&D and I feel comfortable fielding this (this sub gets a lotttt of "whats blindness like" and I would spare people from answering some of those questions if I could)

If the character is just blind in one eye, I'm not sure I'd do anything differently mechanically in D&D. Eyepatches weren't incredibly rare in past ages and maybe someone newly blinded in one eye would get, you know, a temporary -5 on spot checks or something, but then you adjust. Pirates certainly didn't seem concerned about intentionally covering one eye in combat (supposedly this was to help their eyes adjust when they went below deck, too).

Playing a fully blind character would be pretty different than that I think. People's experiences with blindness are different, and it might depend on the character. If your character is a badass ninja, being blind might not be much of a hurdle in close combat and maybe just give them small ranged attack/search penalty. Meanwhile a bookish character might be totally useless in a fight, but maybe they have a great memory and their sense of direction/memory of the room gives them what d&d calls "blindsight," and suddenly the whole party is following them when their last torch runs out :)

You don't need to (and shouldn't) make every blind character into a Daredevil superhero, but it is D&D--remember that a lvl 1 character is essentially an olympic athlete, not a joe-schmoe Medieval peasant

There was a discussion about a fully blind character for DND a few days ago that might be helpful for you to go through but as the previous comment said probably not a whole lot different if it’s only blind in one eye they might want a way to get the DM to describe surroundings in more detail and have a little difficulty with tasks requiring depth perception but that’s not necessary considering it’s dnd also yeah daredevil is ridiculous

Something people not familiar with tabletop RPGs might not be aware of is that Monster of the Week is set in the modern day, I believe in the style of TV shows like Supernatural or Buffy the Vampire Slayer.

That being said, a lot of the advice here still applies. It's worth having a chat with the player and figuring out how they envision the disability impacting their character. I can see it being mostly a gimmick if you aren't careful, or the kind of thing easily forgotten about.

A fully blind monster hunter on the other hand sounds like a really cool concept to play, if I'm honest, but evidently a different one from what this player has in mind.

catching/throwing something always has disadvantage

I'm VI and tried playing DND... It was interesting, lol

I suggest looking up what happens to your sight when you lose one eye. After that, look up the different senses humans have.
Lastly, it's just problem solving from there :)
It's a lot like figuring out how you're going to move a heavy thing when you don't have the physical strength to do so. Think about different methods and test them out.
Even a skilled blind or visually impaired person comes across new problems to solve.
Use that noggin 😊